Which of the following represents a geometric sequence?

Mr. Rawlings had 60 cookies he wanted to give each of his 16 grandchildren the same number of cookies what is the greatest numbe

Solnce55 [7]

He could give each grandchild 3 cookies each. He would then have 12 cookies remaining.

You would divide 60 by 16 which would be 3 with a remainder of 12. The remainder is the number of cookies left after giving each grandchild the same amount of cookies each.

I hope this helps!

3 0

4 years ago

A square park measures 170 feet along each side. Two paved paths run from each corner to the opposite corner and extend 3 feet i

Cerrena [4.2K]

Answer:

The total area, in square feet, taken by the paths is 2,004

Step-by-step explanation:

see the attached figure with lines to better understand the problem

I can divide the figure into four right triangles, one small square and four rectangles

step 1

Find the area of the right triangle of each corner of the path

The area of the triangle is

$A=(1/2)(b)(h)$

substitute the given values

$A=(1/2)(3)(3)=4.5\ ft^2$

step 2

Find the hypotenuse of the right triangle

Applying Pythagoras Theorem

Let

d -----> hypotenuse of the right triangle

$d^{2}=3^{2}+3^{2}$

$d^{2}=18$

$d=\sqrt{18}\ ft$

simplify

$d=3\sqrt{2}\ ft$

The hypotenuse of the right triangle is equal to the width of the path

step 2

Find the area of the small square of the path

The area is

$A=b^{2}$

we have

$b=3\sqrt{2}\ ft$ ----> the width of the path

substitute

$A=(3\sqrt{2})^{2}$

$A=18\ ft^2$

step 3

Find the length of the diagonal of the square park

Applying Pythagoras Theorem

Let

D -----> diagonal of the square park

$D^{2}=170^{2}+170^{2}$

$D^{2}=57,800$

$D=\sqrt{57,800}\ ft$

simplify

$D=170\sqrt{2}\ ft$

step 4

Find the height of each right triangle on each corner

The height will be equal to the width of the path divided by two, because is a 45-90-45 right triangle

$h=1.5\sqrt{2}\ ft$

step 5

Find the area of each rectangle of the path

The area of rectangle is $A=LW$

we have

$W=3\sqrt{2}\ ft$ ----> width of the path

Find the length of each rectangle of the path

$L=(D-2h-d)/2$

where

D is the diagonal of the park

h is the height of the right triangle in the corner

d is the width of the path (length side of the small square of the path)

substitute the values

$L=(170\sqrt{2}-2(1.5\sqrt{2})-3\sqrt{2})/2$

$L=(170\sqrt{2}-3\sqrt{2}-3\sqrt{2})/2$

$L=(164\sqrt{2})/2$

$L=82\sqrt{2}\ ft$

Find the area of each rectangle of the path

$A=LW$

we have

$W=3\sqrt{2}\ ft$

$L=82\sqrt{2}\ ft$

substitute

$A=(82\sqrt{2})(3\sqrt{2})$

$A=492\ ft^2$

step 6

Find the area of the paths

Remember

The total area of the paths is equal to the area of four right triangles, one small square and four rectangles

so

substitute

$A=4(4.5)+18+4(492)=2,004\ ft^2$

therefore

The total area, in square feet, taken by the paths is 2,004

3 0

3 years ago

Please help 1) _____ 2) _____ 3) _____ 4) ____ 5) ____

Luba_88 [7]

Answer:

1 B

2 C

3 E

4 D

5 A

Step-by-step explanation:

1. W is less than Zero

2. W is equal or less than Zero

3. W cannot equal Zero. W is more than Zero or less than Zero

4. W is equal or greater than Zero

5. W is greater than Zero

7 0

3 years ago

Read 2 more answers

School 1: minimum:68, Q1=77, median=83, Q3=86, maximum=95

vlada-n [284]

In school 1, 50% of the students scored above 83 and in school 2, 50% of the class scored above 81.
In school 1, 25% of the students scored above 86 and in school 2, 25% of the class scored above 85.
In school 1, 25% of the students scored below 77 and in school 2, 25% of the class scored below 73.
The minimum score for school 1 is 68 while that of school 2 is 65.
The maximum score for school 1 is 95 while that of school 2 is 98.

In all this measures of center, the data from both schools are close together, so we can conclude that both schools did abut the same on the test.

6 0

3 years ago

Angle Submit Answer 98 85 View One Minute Version Angles - Check My Underst

yulyashka [42]

Answer:

x = 13°

Step-by-step explanation:

Check the diagram attached below to see how the angles labelled A and B, which are interior angles of the triangle where x is found.

Let's find the measure of angle A and angle B.

m<A = 85° (vertical angles are congruent)

m<B = 180° - 98° = 82° (corresponding angles/supplementary angles)

Thus:

x + A + B = 180° (sum of interior angles of a ∆)

x + 85° + 82° = 180° (substitution)

x + 167 = 180

x = 180 - 167 (Subtraction property of equality)

x = 13°

4 0

3 years ago